One-way propagation of light in Born-Infeld-like metamaterials

We propose and investigate a family of nonlinear metamaterials in which light rays propagate just in one direction—one-way propagation. Furthermore, we argue how such nonlinear media could provide an analog model for investigating the Born-Infeld Lagrangian in the realm of fields larger than its scale field.

Figure 1

Normal surfaces [1, 30] for the media with dielectric coefficients given by Eqs. (16) and (17) for $E=1.5b$, $B=1.2b$, and $\alpha =0.5$. Such surfaces are symmetric about the $z$ axis, as clearly seen by Eq. (19). The aforementioned media do not generate ordinary solutions to the Fresnel equation but two extraordinary ones, denoted by “$+$” and “$-$” and depicted by the thick and dot-dashed curves, respectively. If $E>b$, then a region will always exist where the birefringence effect takes place, as clearly shown by Eq. (21) and, for the particular example, encompassed by the two thick straight lines. This region increases when one increases the value of the controllable electric field, as expressed again by Eq. (21). In the complementary region, one refraction and no wave propagation are also present, as depicted between the thick and dashed straight lines and between the two dashed straight lines, respectively.

Figure 2

Ray surfaces [1, 30] for the same medium and parameters as in Fig. 1. As the phase velocities, the group velocities solutions are also symmetric about the $z$ axis. Whenever $E>b$ and Eq. (22) are valid, just a birefringent region exists, as given by Eq. (30). For the previously chosen parameters, such a birefringent region is encompassed by the two thick straight lines. Inside this region, for any direction chosen, just two extraordinary rays are present (related to two different extraordinary waves), denoted by “$+$” and “$-$” and depicted by the thick and dashed curves, respectively; for the set of parameters chosen they are depicted by the thick and dashed curves, respectively. Outside the birefringent region, rays cannot be found. The size of this region decreases with the increase of the electric field.